For each of the following statements, 1. Express the statement using quantifiers 2. Form the negation of the statement (no negation to the left of a quantifier) 3. Translate the negation to simple English (don’t simply state ”it is not the case that...) Assume the domain is all objects in the universe. (a) All games are fun. (b) Some pigs can swim.
For each of the following statements,
1. Express the statement using quantifiers
2. Form the negation of the statement (no negation to the left of a quantifier)
3. Translate the negation to simple English (don’t simply state ”it is not the case that...)
Assume the domain is all objects in the universe.
(a) All games are fun.
(b) Some pigs can swim.
(a) Let us define the following predicates.
game(x) : x is a game
fun(x) : x is fun.
1. The given statement is
" All games are fun. "
≡ ∀x, game(x) => fun(x)
2. Negation of the statement, expressed in symbols is
¬[ ∀x, game(x) => fun(x) ]
≡ ∃x, game(x) ∧ ¬fun(x)
3. Negation of the statement in simple english is
Some game is not fun.
Step by step
Solved in 2 steps
